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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2510.16212 |
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| _version_ | 1866911236000579584 |
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| author | Kaiser, N. |
| author_facet | Kaiser, N. |
| contents | In these notes the Born series for the $s$-wave scattering $a_0$ is calculated for a class of central potentials $V(r)$ up to sixth order in a dimensionless coupling strength $g$. Examples of exponentially decaying potentials as well truncated potentials involving a single length-scale $a$ are considered. In certain favorable cases the exact result for the $g$-dependent $s$-wave scattering length $a_0=A_0(g) a$ can be given in terms of special functions. The poles of $A_0(g)$ at increasing positive values of $g$ correspond to the thresholds, where $s$-wave bound-states occur successively. A scattering problem, where $A_0(g)$ is solvable in terms of elementary functions, is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Born series for s-wave scattering length and some exact results Kaiser, N. Nuclear Theory Quantum Physics In these notes the Born series for the $s$-wave scattering $a_0$ is calculated for a class of central potentials $V(r)$ up to sixth order in a dimensionless coupling strength $g$. Examples of exponentially decaying potentials as well truncated potentials involving a single length-scale $a$ are considered. In certain favorable cases the exact result for the $g$-dependent $s$-wave scattering length $a_0=A_0(g) a$ can be given in terms of special functions. The poles of $A_0(g)$ at increasing positive values of $g$ correspond to the thresholds, where $s$-wave bound-states occur successively. A scattering problem, where $A_0(g)$ is solvable in terms of elementary functions, is also presented. |
| title | Born series for s-wave scattering length and some exact results |
| topic | Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2510.16212 |